Question
Peter has 1200 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area?
Answers
Ms. Sue
It's a square.
Jane
So what exactly would the answer be? im confused..
Ms. Sue
1200/4 = 300 yards on each side.
A = 300 * 300
A = ?
A = 300 * 300
A = ?
Jane
Oh i see now! Ok thank you!
A.
Finding the Absolute Area....
Area of the fence:
A=x*y
Perimeter of the fence
2x+2y=1200
Then, you solve for one variable
2x=1200-2y
x=600-y <-- plug this back into the Area function and you will get
A=(600-y)y
A=600y-y^2
And I believe you can set that equal to zero
-y^2+600y=0
Then you use the quadratic formula
b=600
a=-1
so y= -600/(2)*(-1)
y=300
That'll give you one side, then plug it back to perimeter equation to get x. Hope this is right!
Area of the fence:
A=x*y
Perimeter of the fence
2x+2y=1200
Then, you solve for one variable
2x=1200-2y
x=600-y <-- plug this back into the Area function and you will get
A=(600-y)y
A=600y-y^2
And I believe you can set that equal to zero
-y^2+600y=0
Then you use the quadratic formula
b=600
a=-1
so y= -600/(2)*(-1)
y=300
That'll give you one side, then plug it back to perimeter equation to get x. Hope this is right!
Ms. Sue
You're welcome.